Roberto wrote to me:

Debian policy actually
specifically addresses private libraries:

> Shared object files (often .so files) that are not public libraries,
> that is, they are not meant to be linked to by third party
> executables (binaries of other packages), should be installed in
> subdirectories of the /usr/lib directory. Such files are exempt from
> the rules that govern ordinary shared libraries, except that they
> must not be installed executable and should be stripped.

Additionally, lintian also complains:

W: libmongoc-priv: package-name-doesnt-match-sonames libmongoc-priv0

I think that it would make sense for you to update the upstream part of
the build system to install the -priv library into something like
/usr/lib/<arch>/mongoc

It would also be a good idea to get the upstream build system to not
install the .so.0 and .so.0.0.0 symlinks if the -priv library really
doesn't have a SONAME.

The policy is here:

https://www.debian.org/doc/debian-policy/ch-files.html#s-libraries

Currently our "debian" branch has some patches to make the package meet Debian's policy. But assuming the Debian policy is a good policy for installing a private runtime library on any Linux distro, we should update our "make install" to match, and then revert the patches in the "debian" branch.